Influence analyses of skew-normal/independent linear mixed models

A extension of some diagnostic procedures to skew-normal/independent linear mixed models is discussed. This class provides a useful generalization of normal (and skew-normal) linear mixed models since it is assumed that the random effects and the random error terms follow jointly a multivariate skew-normal/independent distribution. Inspired by the EM algorithm, a local influence analysis for linear mixed models, following Zhu and Lee’s approach is developed. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex and Cook’s well-known approach can be very difficult for obtaining measures of local influence. Moreover, the local influence measures obtained under this approach are invariant under reparameterization. Four specific perturbation schemes are also discussed. Finally, a real data set is analyzed in order to illustrate the usefulness of the proposed methodology.